@article {549,
	title = {Subspace Averaging and Order Determination for Source Enumeration},
	journal = {IEEE Transactions on Signal Processing},
	volume = {67},
	year = {2019},
	month = {June},
	pages = {3028-3041},
	abstract = {In this paper we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally-determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.},
	doi = {10.1109/TSP.2019.2912151},
	author = {Garg, Vaibhav and Santamar{\'\i}a, Ignacio and Ram{\'\i}rez, David and Louis L. Scharf}
}
@article {596,
	title = {Scale-Invariant Subspace Detectors based on First and Second-Order Statistical Models},
	journal = {IEEE Transactions on Signal Processing},
	volume = {68},
	year = {2020},
	pages = {6432-6443},
	doi = {10.1109/TSP.2020.3036725},
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and Ram{\'\i}rez, David}
}
@article {494,
	title = {Passive Detection of Correlated Subspace Signals in Two MIMO Channels},
	journal = {IEEE Transactions on Signal Processing},
	volume = {65},
	year = {2017},
	month = {October},
	pages = {5266-5280},
	doi = {10.1109/TSP.2017.2723340},
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and V{\'\i}a, Javier and Wang, Yuan and Wang, Haonan}
}
@article {568,
	title = {Multi-Channel Factor Analysis with Common and Unique Factors},
	journal = {IEEE Transactions on Signal Processing},
	volume = {68},
	year = {2020},
	pages = {113-126},
	abstract = {This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.},
	issn = {1053-587X},
	doi = {10.1109/TSP.2019.2955829},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Louis L. Scharf and Van Vaerenbergh, Steven}
}
@article {340,
	title = {Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors},
	journal = {IEEE Transactions on Information Theory},
	volume = {59},
	year = {2013},
	month = {April},
	pages = {2128{\textendash}2141},
	abstract = {In this paper we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman{\textquoteright}s theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set of N-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts.},
	doi = {10.1109/TIT.2012.2232705},
	author = {Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@article {GLRT_GCS_Detection_Spatially_TrSP,
	title = {Detection of Spatially Correlated Gaussian Time Series},
	journal = {IEEE Transactions on Signal Processing},
	volume = {58},
	number = {10},
	year = {2010},
	month = {October},
	pages = {5006{\textendash}5015},
	author = {Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@article {453,
	title = {Detection of Multivariate Cyclostationarity},
	journal = {IEEE Transactions on Signal Processing},
	volume = {63},
	year = {2015},
	month = {October},
	pages = {5395-5408},
	abstract = {This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover,
using Wijsman{\textquoteright}s theorem, we also obtain an asymptotic LMPIT.
These detectors may be expressed in terms of the Lo{\`e}ve spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic
GLRT and LMPIT. This goes beyond the state of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {560,
	title = {Subspace Averaging in Multi-Sensor Array Processing},
	booktitle = {SIAM Conference on Applied Algebraic Geometry},
	year = {2019},
	month = {July},
	address = {Bern, Switzerland},
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and Garg, Vaibhav and Ram{\'\i}rez, David}
}
@conference {514,
	title = {Subspace Averaging for Source Enumeration in Large Arrays},
	booktitle = {IEEE Statistical Signal Processing Workshop (SSP)},
	year = {2018},
	month = {June},
	address = {Freiburg, Germany},
	abstract = {Subspace averaging is proposed and examined as a method of enumerating sources in large linear arrays, under conditions of low sample support. The key idea is to exploit shift invariance as a way of
extracting many subspaces, which may then be approximated by a
single extrinsic average. An automatic order determination rule for
this extrinsic average is then the rule for determining the number
of sources. Experimental results are presented for cases where the
number of array snapshots is roughly half the number of array elements, and sources are well separated with respect to the Rayleigh
limit.},
	author = {Santamar{\'\i}a, Ignacio and Ram{\'\i}rez, David and Louis L. Scharf}
}
@conference {424,
	title = {A Regularized Maximum Likelihood Estimator for the Period of a Cyclostationary Process},
	booktitle = {Asilomar Conference on Signals, Systems, and Computers},
	year = {2014},
	month = {November},
	address = {Pacific Grove, USA},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {475,
	title = {Passive Detection of Rank-One Signals with a Multiantenna Reference Channel},
	booktitle = { 24th European Signal Processing Conference (EUSIPCO 2016)},
	year = {2016},
	month = {September},
	pages = {140-144},
	address = {Budapest, Hungary},
	abstract = {In this work we consider a two-channel passive detection problem,
in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.},
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and Cochran, D. and V{\'\i}a, Javier}
}
@conference {641,
	title = {Passive Detection of Rank-one Gaussian Signals for Known Channel Subspaces and Arbitrary Noise},
	booktitle = {IEEE International Conference on Acoustics Speech and Signal Processing},
	year = {2023},
	month = {June},
	address = {Rhodes, Greece},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {466,
	title = {An order fitting rule for optimal subspace averaging},
	booktitle = {IEEE Workshop on Statistical Signal Processing (SSP)},
	year = {2016},
	month = {June },
	address = {Palma de Mallorca},
	abstract = {The problem of estimating a low-dimensional subspace from a collection of experimentally measured subspaces arises in many applications of statistical signal processing. In this paper we address this problem, and give a solution for the average subspace that minimizes an extrinsic mean-squared error, defined by the squared Frobenius norm between projection matrices. The solution automatically returns the dimension of the optimal average subspace, which is the novel result of the paper. The proposed order fitting rule is based on thresholding the eigenvalues of the average projection matrix, and thus it is free of penalty terms or other tuning parameters commonly used by other rank estimation techniques. Several numerical examples demonstrate the usefulness and applicability of the proposed criterion, showing how the dimension of the average subspace captures the variability of the measured subspaces. },
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and Peterson, Chris and Kirby, Michael and Francos, Joseph}
}
@conference {SSPNice2011_ML_beamsteering,
	title = {Multi-Sensor Beamsteering Based on the Asymptotic Likelihood for Colored Signals},
	booktitle = {IEEE Workshop on Statistical Signal Processing (SSP 2011)},
	year = {2011},
	month = {June},
	address = {Nice, France},
	author = {Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {ICASSP2011Prague_GLRT_flat_fading,
	title = {Multiple-Channel Detection of a Gaussian Time Series over Frequency-Flat Channels},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)},
	year = {2011},
	month = {May},
	address = {Prague, Czech Republic},
	author = {Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {ICASSP2010_CR_SpecSensing,
	title = {Multiantenna Spectrum Sensing: Detection of Spatial Correlation Among Time-Series With Unknown Spectra},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010)},
	year = {2010},
	month = {March},
	address = {Dallas, USA},
	author = {Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and L{\'o}pez-Valcarce, Roberto and Louis L. Scharf}
}
@conference {309,
	title = {The Locally Most Powerful Invariant Test for Detecting a Rank-P Gaussian Signal in White Noise},
	booktitle = {7th IEEE Sensor Array and Multichannel Signal Processing Workshop},
	year = {2012},
	month = {June},
	address = {Hoboken, NJ, USA},
	abstract = {Spectrum sensing has become one of the main components of a cognitive transmitter. Conventional detectors suffer from noise power uncertainties and multiantenna detectors have been proposed to overcome this difficulty, and to improve the detection performance. However, most of the proposed multiantenna detectors are based on non-optimal techniques, such as the generalized likelihood ratio test (GLRT), or even heuristic approaches that are not based on first principles. In this work, we derive the locally most powerful invariant test (LMPIT), that is, the optimal invariant detector for close hypotheses, or equivalently, for a low signal-to-noise ratio (SNR). The traditional approach, based on the distributions of the maximal invariant statistic, is avoided thanks to Wijsman{\textquoteright}s theorem, which does not need these distributions. Our findings show that, in the low SNR regime, and in contrast to the GLRT, the additional spatial structure imposed by the signal model is irrelevant for optimal detection. Finally, we use Monte Carlo simulations to illustrate the good performance of the LMPIT.},
	author = {Ram{\'\i}rez, David and Iscar, Jorge and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {661,
	title = {Identifiability in Multi-Channel Factor Analysis},
	booktitle = {Asilomar Conference on Signals, Systems, and Computers},
	year = {2023},
	month = {November},
	address = {Pacific Grove, CA, USA},
	author = {Stanton, Gray and Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Louis L. Scharf and Wang, Haonan}
}
@conference {491,
	title = {A GLRT approach for detecting correlated signals in white noise in two MIMO channels},
	booktitle = {European Signal Processing Conference (EUSIPCO)},
	year = {2017},
	month = {August},
	address = {Kos, Greece},
	author = {Santamar{\'\i}a, Ignacio and V{\'\i}a, Javier and Louis L. Scharf and Wang, Yuan}
}
@conference {469,
	title = {Estimating the mean manifold of a deformable object from noisy observations},
	booktitle = {IEEE Image Video and Multidimensional Signal Processing Workshop (IVMSP) },
	year = {2016},
	month = {July},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Bordeaux,France},
	abstract = {Assume we have a set of noisy observations (for example, images) of different objects, each undergoing a different
geometric deformation, yet all the deformations belong to the same family. As a result of the action of these deformations,
the set of different observations on each object is generally a manifold in the ambient space of observations. It has been shown, [1], that in the absence of noise, in those cases where the set
of deformations admits a finite-dimensional representation, the universal manifold embedding (UME) provides a mapping from the space of observations to a low dimensional linear space. The
manifold corresponding to each object is mapped to a distinct linear subspace of Euclidean space, and the dimension of the
subspace is the same as that of the manifold. In the presence of noise, different observations are mapped to different subspaces. In this paper we derive a method for {\textquotedblleft}averaging{\textquotedblright} the different subspaces, obtained from different observations made on the same object, in order to estimate the mean representation of the object manifold. The mean manifold representation is then employed to minimize the effects of noise in matched manifold detectors and to improve the separability of data sets in the context of object detection and classification.},
	author = {Yavo, Z and Francos, Joseph and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {492,
	title = {Constrained subspace estimation via convex optimization},
	booktitle = {European Signal Processing Conference (EUSIPCO)},
	year = {2017},
	month = {August},
	address = {Kos, Greece},
	author = {Santamar{\'\i}a, Ignacio and V{\'\i}a, Javier and Kirby, Michael and Marrinan, Timothy and Peterson, Chris and Louis L. Scharf}
}
@conference {481,
	title = {Canonical Correlations for Target Detection in a Passive Radar Network},
	booktitle = {Asilomar Conference on Signals, Systems and Computers (ASILOMAR)},
	year = {2016},
	month = {November},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Pacific Grove (CA), USA},
	author = {Wang, Yuan and Louis L. Scharf and Santamar{\'\i}a, Ignacio and Wang, Haonan}
}
@conference {433,
	title = {An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2015},
	month = {April},
	address = {Brisbane, Australia},
	author = {Ram{\'\i}rez, David and Schreier, Peter J. and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
@conference {388,
	title = {An asymptotic GLRT for the detection of cyclostationary signals},
	booktitle = {International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
	year = {2014},
	month = {May},
	address = {Florence, Italy},
	author = {Ram{\'\i}rez, David and Louis L. Scharf and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio and Schreier, Peter J.}
}
@conference {518,
	title = {An alternating optimization algorithm for two-channel factor analysis with common and uncommon factors},
	booktitle = {52nd Asilomar Conference on Signals, Systems and Computers},
	year = {2018},
	month = {October},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Pacific Grove (CA), USA},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Van Vaerenbergh, Steven and Louis L. Scharf}
}
@book {633,
	title = {Coherence in Signal Processing and Machine Learning},
	year = {2022},
	publisher = {Springer},
	organization = {Springer},
	isbn = {978-3-031-13330-5},
	doi = {https://doi.org/10.1007/978-3-031-13331-2},
	url = { https://link.springer.com/book/10.1007/978-3-031-13331-2},
	author = {Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio and Louis L. Scharf}
}
